Toward Mathematical Intelligence and Certifiable Automated Reasoning: From Theoretical Foundations to Experimental Realization
Abstract
Quantum field theory is the foundation of modern science, and it remains the best experimentally-verified model of the real world. A second quantum revolution is under way, in and around the construction of a certifiable quantum computer. This builds on the visionary insights of the mathematician Yu. Manin and physicist R. Feynman, and it provides the potential to transform every aspect of human society. We propose to investigate and to develop mathematical insights combining picture calculus, quantum logic, quantum field theory, and related questions. These ideas have already proved relevant in quantum information, and among our goals are to investigate protocols, algorithms, complexity, error correction, and the certifiability of quantum processes. What makes our proposal unique is our linking extremely abstract, theoretical ideas with practical laboratory implementation. Therefore, our collaboration includes both leading experts in different frontiers of mathematics and theoretical physics, but also one of the leading experts in the experimental implementation of qubits. Our project emphasizes team effort and cooperation between team members with widely disparate, interdisciplinary backgrounds. All our team members have records of past success in their own domains, as well as demonstrated interest in crossing intellectual boundaries. We have assembled a team composed of leading groups, at Harvard University, Johns Hopkins University, and the University of California at Santa Barbara, with other team members at New Mexico State University, Purdue University, and the University of Tennessee. Developing efficient and implementable algorithms to deal with errors is one of the most important issues to enable the construction of a quantum computer. Preliminary work indicates that our methods could substantially improve present error correction codes. We plan to focus our theoretical-experimental connection on discovering, developing, and testing the viability of new methods for quantum error correction. We will work toward the unified goal of providing a rigorous theory for mathematicallyintelligent machines. Our outputs promise to be theoretically significant as well as practically implementable. Our team is enthusiastic about the interdisciplinary synergy that we have already begun to generate to envision testing our new theoretical methods in the laboratory. The ideas rely on diverse scientific threads which lie at the outer frontiers of researchÑboth in theoretical mathematics and also in experimental physics. The groups in our team represent key pieces in the design of an intelligent machine. Such a project must be based on quantum logic (proposed by Birkhoff and von Neumann), namely the study of the lattice of certain subspaces of a Hilbert space. This is embodied in higher category theory, homotopy type theory, and planar algebras. It is conjectured that higher category theory leads to a new type of quantum logic. Our pictorial languages have given new insight into questions of quantum information, and we believe that they will result in important future progress.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jul 09, 2020
- Source ID
- W911NF2010082
Entities
People
- Arthur Jaffe
Organizations
- Army Contracting Command
- Harvard University
- United States Army